''Blacks in America,'' Neil deGrasse Tyson remembers a college classmate lecturing him, ''do not have the luxury of your intellectual talents being spent on astrophysics.'' That moment presented a conflict for an idealistic young scientist with his mind on the universe. Nine years later, when he was a graduate student at Columbia University, Tyson appeared on a cable news program to explain the implications of some recent solar explosions. Watching the broadcast, Tyson concluded that it was not a matter of the black community's suffering because he became a scientist, but that ''the black community cannot afford it if I don't.'' When he received his Ph.D., Tyson became only the seventh black astrophysicist in the United States. ''The Sky Is Not the Limit'' is a hybrid: part scientific autobiography, part scratchpad of astrophysics topics in the news. Tyson, currently the director of the Hayden Planetarium, leaps quickly from idea to idea: the decline of public interest in space and prospects for a reinvigorated space program, theories about heat death and cataclysmic end-days scenarios of an asteroid colliding with the earth, the relationship between science and religion. All this is interesting, but the book is strongest when Tyson connects his personal experiences to the development of his professional career. Scott Gabriel Knowles